A Necessary and Sufficient Stability Condition of Discrete-Time Monotone Systems: A Max-Separable Lyapunov Function Method

Addressed in this paper is the stability issue of discrete-time monotone nonlinear systems. With the assumption of the considered vector field being a one-to-one mapping, we established the equivalence between the locally asymptotic stability and the existence of a max-separable Lyapunov function on a compact set. This result is an extension of that of discrete-time monotone linear systems. Furthermore, it is a counterpart of continuous-time monotone nonlinear systems.